Research On Theoretical Modeling And Static Characteristics Of Gas Foil Bearings Based On Frictional Contacts

Compared with rigid gas bearings,gas foil bearings have many advantages,such as high running speed,wide temperature operation ranges,high structural damping and the ability to accommodate larger misalignment.Therefore,they have an important application value in some rotating machinery devices such as gas compressors and microturbines.Accurate predictions of the static and dynamic performances are very important to the design of the foil bearings.However,due to the relatively complex structure of the foil bearings,there still exist a lot of difficulties at present,especially the frictional contact behavior of the foil structure has not been adequately studied.Based on the contact mechanics and the finite element theory,a two-dimensional model and a three-dimensional model of the foil bearings were theoretically established in this paper.The nonlinear behavior of the frictional contacts of the foil structure was considered,and the static characteristics of foil bearings were studied.The main contents of this paper are as follows:(1)The finite difference method was used to solve the Reynolds equation.Combined with the relaxation iterative method,the calculation formula for gas film pressure of the aerodynamic bearing was deduced.The gas film pressure and film thickness distributions of a rigid gas bearing were obtained.This numerical model was verified by comparisons with the literature data,and its iterative convergence characteristics were also studied.(2)Based on the contact mechanics,the penalty method and the Coulomb friction law were used to establish the nonlinear model of the frictional contacts of the foil structure,considering the three different contact states(separation,stick and slip).Since the contact behavior was related to time or path,the incremental iterative method was utilized for solution of the finite element equilibrium equation of the foil structure,in which the calculation in the present step was based on the results from the previous step.The calculation formulas for normal contact force and tangential friction force in different contact states were deduced in detail.The checking conditions and the solution process of contact problems were given.The results showed that this contact model could well capture the nonlinear behavior of the frictional contacts.(3)Based on the finite element theory,the beam elements were used to discretize the top foil and the bump foil.Combined with the nonlinear model of frictional contacts,a nonlinear two-dimensional model of the foil structure was established,which was also coupled with the gas film pressure.This model comprehensively considered the elasticity of the bump foil,the interactions between adjacent bumps,the local deflection of the top foil,the nonlinear frictional contacts and the aeroelastic coupling effect.The film pressure distribution,film thickness,relationship between minimum film thickness and load,energy dissipation characteristics of the foil bearing were studied by using this model under the static conditions.The simulation results showed that the deformation of the foil structure exhibited the hysteresis effect due to the existence of friction.And the friction coefficient affected the energy dissipation characteristics of the foil bearing.(4)A three-dimensional structural model of the foil bearing was established by using the shell elements.The shell element was obtained by combining the plane element and the plate element;hence,the membrane,bending and shear effects of the foil structure were considered.To enhance the convergence of the algorithm,a regularization technique was utilized to modify the Coulomb friction law.The calculation formula for contact forces was deduced.Due to the nonlinearity of frictional contacts,the incremental iterative method was also used to solve the finite element equilibrium equation of the foil structure.The effect of rotor misalignment on the static performance of the foil bearing was studied.The results showed that rotor misalignment greatly reduced the loading capacity of the foil bearing.In addition,the minimum film thickness and structural deformation of the first and second generation foil bearings considering misalignment were investigated,which showed that the second generation foil bearing had the ability to accommodate larger misalignment.